We propose a modified discrete-time Leslie-Gower competition system of two popula- tions to study competition outcomes. Depending on the magnitude of a particular model parameter that measures intraspecific competitio...We propose a modified discrete-time Leslie-Gower competition system of two popula- tions to study competition outcomes. Depending on the magnitude of a particular model parameter that measures intraspecific competition between individuals within the same population, either one or both populations may be subject to Allee effects. The resulting system can have up to four coexisting steady states. Using the theory of planar compet- itive maps, it is shown that the model has only equilibrium dynamics. The competition outcomes then depend not only on the parameter regimes but may also depend on the initial population distributions.展开更多
In the real world, the population systems are often subject to white noises and a system with such stochastic perturbations tends to be suitably modeled by stochastic differential equations. This paper is concerned wi...In the real world, the population systems are often subject to white noises and a system with such stochastic perturbations tends to be suitably modeled by stochastic differential equations. This paper is concerned with the dynamic behaviors of a delay stochastic competitive system. We first obtain the global existence of a unique positive solution of system. Later, we show that the solution of system will be stochastically ultimate boundedness. However, large noises may make the system extinct exponentially with probability one. Also, sufficient conditions for the global attractivity of system are established. FinMly, illustrated examples are given to show the effectiveness of the proposed criteria.展开更多
A competitive system on the n-rectangle： {x ∈ Rn： 0 ≤ xi ≤ li, i = 1,... ,n} was con- sidered, each species of which, in isolation, admits logistic growth with the hyperbolic structure saturation. It has an （n ...A competitive system on the n-rectangle： {x ∈ Rn： 0 ≤ xi ≤ li, i = 1,... ,n} was con- sidered, each species of which, in isolation, admits logistic growth with the hyperbolic structure saturation. It has an （n - 1）-dimensional invariant surface called carrying simplex E as a globe attractor, hence the long term dynamics of the system is com- pletely determined by the dynamics on E. For the three-dimensional system, the whole dynamical behavior was presented. It has a unique positive equilibrium point and any limit set is either an equilibrium point or a limit cycle. The system is permanent and it is proved that the number of periodic orbits is finite and non-periodic oscillation the May Leonard phenomenon does not exist. A criterion for the positive equilibrium to be globally asymptotically stable is provided. Whether there exist limit cycles or not remains open.展开更多
文摘We propose a modified discrete-time Leslie-Gower competition system of two popula- tions to study competition outcomes. Depending on the magnitude of a particular model parameter that measures intraspecific competition between individuals within the same population, either one or both populations may be subject to Allee effects. The resulting system can have up to four coexisting steady states. Using the theory of planar compet- itive maps, it is shown that the model has only equilibrium dynamics. The competition outcomes then depend not only on the parameter regimes but may also depend on the initial population distributions.
基金Acknowledgments The authors thank the referees for their reports and many valuable comments and suggestions that greatly improved the presentation of this paper. The work is supported by the National Natural Science Foundation of China （No. 11261017）, the Key Laboratory of Biological Resources Protection and Utilization of Hubei Province （No. PKLHB1323） and the Key Project of Chinese Ministry of Education （No. 212111）.
文摘In the real world, the population systems are often subject to white noises and a system with such stochastic perturbations tends to be suitably modeled by stochastic differential equations. This paper is concerned with the dynamic behaviors of a delay stochastic competitive system. We first obtain the global existence of a unique positive solution of system. Later, we show that the solution of system will be stochastically ultimate boundedness. However, large noises may make the system extinct exponentially with probability one. Also, sufficient conditions for the global attractivity of system are established. FinMly, illustrated examples are given to show the effectiveness of the proposed criteria.
文摘A competitive system on the n-rectangle： {x ∈ Rn： 0 ≤ xi ≤ li, i = 1,... ,n} was con- sidered, each species of which, in isolation, admits logistic growth with the hyperbolic structure saturation. It has an （n - 1）-dimensional invariant surface called carrying simplex E as a globe attractor, hence the long term dynamics of the system is com- pletely determined by the dynamics on E. For the three-dimensional system, the whole dynamical behavior was presented. It has a unique positive equilibrium point and any limit set is either an equilibrium point or a limit cycle. The system is permanent and it is proved that the number of periodic orbits is finite and non-periodic oscillation the May Leonard phenomenon does not exist. A criterion for the positive equilibrium to be globally asymptotically stable is provided. Whether there exist limit cycles or not remains open.
